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| 1. |
4xsquare -4ax +(asquare - bsquare)=0 |
| Answer» According to the question,\xa0{tex}4 x^{2}-4 a x+\\left(a^{2}-b^{2}\\right)=0{/tex}{tex}\\Rightarrow x^{2}-a x+\\left(\\frac{a^{2}-b^{2}}{4}\\right)=0{/tex}{tex}\\Rightarrow x^{2}-2\\left(\\frac{a}{2}\\right) x=-\\left(\\frac{a^{2}-b^{2}}{4}\\right){/tex}{tex}\\Rightarrow x^{2}-2\\left(\\frac{a}{2}\\right) x+\\left(\\frac{a}{2}\\right)^{2}{/tex}=\xa0{tex}-\\left(\\frac{a^{2}-b^{2}}{4}\\right)+\\left(\\frac{a}{2}\\right)^{2}{/tex}{tex}\\Rightarrow\\left(x-\\frac{a}{2}\\right)^{2}{/tex}\xa0=\xa0{tex}-\\frac{a^{2}}{4}+\\frac{b^{2}}{4}+\\frac{a^{2}}{4}{/tex}{tex}\\Rightarrow\\left(x-\\frac{a}{2}\\right)^{2}=\\frac{b^{2}}{4}{/tex}{tex}\\Rightarrow x-\\frac{a}{2}=\\pm \\frac{b}{2}{/tex}\xa0{tex}\\therefore{/tex}\xa0x =\xa0{tex}\\frac{a+b}{2}{/tex},\xa0{tex}\\frac{a-b}{2}{/tex} | |